Geodesic
On the Spectrum of Sets Made of Cores and Tubes
Journal of convex analysis, Tome 31 (2024) no. 2, pp. 315-358
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We analyze the spectral properties of a particular class of unbounded open sets. These are made of a central bounded "core", with finitely many unbounded tubes attached to it. We adopt an elementary and purely variational point of view, studying the compactness (or the defect of compactness) of level sets of the relevant constrained Dirichlet integral. As a byproduct of our argument, we also get exponential decay at infinity of variational eigenfunctions. Our analysis includes as a particular case a planar set (sometimes called "bookcover"), already encountered in the literature on curved quantum waveguides. J. Hersch suggested that this set could provide the sharp constant in the Makai-Hayman inequality for the bottom of the spectrum of the Dirichlet-Laplacian of planar simply connected sets. We disprove this fact, by means of a singular perturbation technique.
Classification : 35P15, 35B38, 58E05
Mots-clés : Eigenvalue estimates, Poincaré inequality, inradius, Makai-Hayman inequality, Palais-Smale sequence, curved waveguide 
@article{JCA_2024_31_2_JCA_2024_31_2_a2,
     author = {F. Bianchi and L. Brasco and R. Ognibene},
     title = {On the {Spectrum} of {Sets} {Made} of {Cores} and {Tubes}},
     journal = {Journal of convex analysis},
     pages = {315--358},
     year = {2024},
     volume = {31},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2024_31_2_JCA_2024_31_2_a2/}
}
TY  - JOUR
AU  - F. Bianchi
AU  - L. Brasco
AU  - R. Ognibene
TI  - On the Spectrum of Sets Made of Cores and Tubes
JO  - Journal of convex analysis
PY  - 2024
SP  - 315
EP  - 358
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JCA_2024_31_2_JCA_2024_31_2_a2/
ID  - JCA_2024_31_2_JCA_2024_31_2_a2
ER  - 
%0 Journal Article
%A F. Bianchi
%A L. Brasco
%A R. Ognibene
%T On the Spectrum of Sets Made of Cores and Tubes
%J Journal of convex analysis
%D 2024
%P 315-358
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/JCA_2024_31_2_JCA_2024_31_2_a2/
%F JCA_2024_31_2_JCA_2024_31_2_a2
F. Bianchi; L. Brasco; R. Ognibene. On the Spectrum of Sets Made of Cores and Tubes. Journal of convex analysis, Tome 31 (2024) no. 2, pp. 315-358. http://geodesic.mathdoc.fr/item/JCA_2024_31_2_JCA_2024_31_2_a2/